Landweber–Kaczmarz for parameter identification in time-dependent inverse problems: all-at-once versus reduced version. (5th February 2019)

• Record Type: Journal Article
• Authors: Nguyen, Tram Thi Ngoc
• Is Part Of: Inverse problems. Volume 35:Number 3(2019)
• Publication Date: 2019-02-05
• Subjects: time dependent inverse problems -- nonlinear source identification -- Kaczmarz method -- parameter identification -- iterative regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaf9ba
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this study, we consider a general time-space system, whose model operator and observation operator are locally Lipschitz continuous, over a finite time horizon and parameter identification by using Landweber–Kaczmarz regularization. The problem is investigated in two different modeling settings: an all-at-once and a reduced version, together with two observation scenarios: continuous and discrete observations. Segmenting the time line into several subintervals leads to the idea of applying the Kaczmarz method. A loping strategy is incorporated into the method to yield the loping Landweber–Kaczmarz iteration.